Heun's method: Difference between revisions

Revision as of 11:49, 28 January 2012

Revision as of 15:36, 13 March 2012

Line 1:

In [[mathematics]] and [[computational science]], '''Heun's method''' may refer to the '''improved'''<ref>{{Citation | last1=Süli | first1=Endre | last2=Mayers | first2=David | title=An Introduction to Numerical Analysis | publisher=[[Cambridge University Press]] | isbn=0521007941 | year=2003}}.</ref> or '''modified Euler's method''' (that is, the '''explicit trapezoidal rule'''<ref>

{{Citation | last1=Ascher | first1=Uri M. | last2=Petzold | first2=Linda R. | title=Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations | publisher=[[Society for Industrial and Applied Mathematics]] | ___location=Philadelphia | isbn=978-0-89871-412-8 | year=1998}}.</ref>), or a similar two-stage [[Runge–Kutta method]]. It is named after [[Karl L. W. M. Heun]] and is a [[numerical analysis|numerical]] procedure for solving [[Ordinary_differential_equation|ordinary differential equations]] (ODEs) with a given [[Initial_value_problem|initial value]]. Both variants can be seen as extensions of the [[Euler method]] into two-stage second-order Runge–Kutta methods.